AN-1152
APPLICATION NOTE
One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106, U.S.A. • Tel: 781.329.4700 • Fax: 781.461.3113 • www.analog.com
Calibrating a Single-Phase Energy Meter Based on the ADE7816
by Aileen Ritchie
INTRODUCTION
This application note describes how to calibrate the ADE7816.
It details the calibration procedure, including equations and
examples of how to calculate each constant.
The ADE7816 is a high accuracy multichannel metering IC that
allows the energy to be measured on up to six current channels.
It provides a variety of energy measurements including active
and reactive energy, along with current and voltage rms readings.
A variety of power quality features, including no load, reverse
power, and angle measurement, are also provided. The ADE7816
can be accessed via an SPI, I2C, or high speed data capture
(HSDC) interface.
Rev. 0 | Page 1 of 12
AN-1152
Application Note
TABLE OF CONTENTS
Introduction ...................................................................................... 1
Phase Calibration ..........................................................................5
Revision History ............................................................................... 2
Establishing the Wh/LSB Constant—First Meter Only ...........6
Calibration Basics ............................................................................. 3
Active Energy Gain Calibration ..................................................6
Calibration Steps........................................................................... 3
Reactive Energy Gain Calibration...............................................7
Calibration Setup .......................................................................... 3
Advanced Energy Offset Calibration (Optional) ......................7
Required Register Settings .......................................................... 4
Current and Voltage RMS ............................................................8
Energy Calibration ........................................................................... 5
Current Channel Gain Matching ............................................... 5
REVISION HISTORY
5/12—Revision 0: Initial Version
Rev. 0 | Page 2 of 12
Application Note
AN-1152
CALIBRATION BASICS
The active and reactive energies, along with current and voltage
rms, must be calibrated for accurate readings to be acquired.
All signal paths are independent and, therefore, perform the
calibration on the measurements that are required in the
completed meter.
CALIBRATION SETUP
Accurate Source
To calibrate the ADE7816, an accurate source should be used.
The accurate source must be able to provide a controllable
voltage and current input with higher accuracy than that
required in the resulting meter. Figure 1 shows a typical setup
using an accurate source.
THE SOURCE PROVIDES THE
ACCURACY FOR CALIBRATION
Access to the energy metering registers is provided via the SPI
or I2C interface (see the ADE7816 data sheet for more details).
When calibrating the active and reactive energy readings, the
line cycle accumulation mode should be used. See the ADE7816
data sheet for details on the line cycle accumulation mode.
CURRENT ×6
SOURCE
CALIBRATION STEPS
VOLTAGE
When designing a meter using the ADE7816, a maximum of
three calibration stages is required: gain, phase, and offset.
These stages must be performed on each measurement separately. Depending on the external configuration and meter class,
one or more of these stages can be omitted. Table 1 provides
guidance on which calibration steps are typically required for a
particular configuration. Because the requirements and performance can differ on a design-by-design basis, use Table 1 as a
general guideline only. The performance of the meter should be
evaluated to determine whether any additional calibration steps
are required.
Table 1. Typical Calibration Steps
Calibration Stage
Gain Calibration
Phase Calibration
Offset Calibration
Typical Requirement
It is always required.
It is required when using a sensor that
introduces a phase delay.
If the sensor does not introduce a phase
delay, it is not typically required.
When looking for high accuracy over a
large dynamic range, it is often required.
It is not usually required for all other meter
designs.
10668-001
To obtain accurate readings that do not reflect meter-to-meter
variations in external components or the internal voltage reference,
the ADE7816 requires calibration. Calibration is required on
every meter; however, it is a simple process that can be performed
quickly.
Figure 1. Accurate Source
Ideally, calibrate all six current channels simultaneously. If this
is not possible, each channel can be calibrated individually. Care
should be taken to isolate and verify the board level channel-tochannel crosstalk for optimum performance.
Required Input Conditions
The gain and phase calibration steps can be performed with a
single set of inputs. Set the voltage to the nominal value, typically 110 V or 220 V. The current should also be set to the
nominal value, for example, 10 A. It is advisable to set the
current around 10 times less than the maximum current for
the meter. The current and voltage inputs should be applied
at a power of around 0.5. The load can be either capacitive or
inductive. The key factor when setting up the calibration inputs
is to determine exactly what is being applied to the meter. For
example, there is no issue in using a power factor of 0.45 as long
as it is known that this is what is being applied to the meter.
If an offset calibration step is required, a second load must be
applied at the minimum current. The voltage should remain at
nominal level and the power factor at 0.5.
Rev. 0 | Page 3 of 12
AN-1152
Application Note
REQUIRED REGISTER SETTINGS
Prior to calibrating the ADE7816, it is important that a set of
default registers be configured. These registers are listed in
Table 2. Refer to the ADE7816 data sheet for details on these
registers.
Table 2. Default Registers Required Prior to Calibration
Register Address
0x43AB
0x43AC
0x43AD
0x43AE
0x43B1
0x43B2
0x43B3
0x43B4
0x43B5
0x43B6
0x4388
Register Name
WTHR1
WTHR0
VARTHR1
VARTHR0
PCF_A_COEFF
PCF_B_COEFF
PCF_C_COEFF
PCF_D_COEFF
PCF_E_COEFF
PCF_F_COEFF
DICOEFF
Register Description
Threshold register for active energy
Threshold register for active energy
Threshold register for reactive energy
Threshold register for reactive energy
Phase calibration for Current Channel A
Phase calibration for Current Channel B
Phase calibration for Current Channel C
Phase calibration for Current Channel D
Phase calibration for Current Channel E
Phase calibration for Current Channel F
Digital integrator algorithm; required only if using di/dt sensors
Rev. 0 | Page 4 of 12
Required Value
0x000002
0x000000
0x000002
0x000000
0x400CA4 (50 Hz)
0x400CA4 (50 Hz)
0x400CA4 (50 Hz)
0x400CA4 (50 Hz)
0x400CA4 (50 Hz)
0x400CA4 (50 Hz)
0xFFF8000
Application Note
AN-1152
ENERGY CALIBRATION
CURRENT CHANNEL GAIN MATCHING
Figure 2 shows the calibration flow for the energy measurements. Use this flow to determine a calibration routine.
Because the ADE7816 has six current channels, it is convenient
to match them all prior to calibrating. Matching the current
channels results in easier computations because one bit in the
rms and energy registers has the same weight on each channel.
It is recommended that channel matching be performed as the
first calibration step.
START
CALIBRATION
SET
IxGAIN
SEE CURRENT
CHANNEL
GAIN MATCHING
SECTION
To match the six current channels, follow the procedure
outlined in the Setting the IxGain Registers section.
Setting the IxGain Registers
CALIBRATE
PCF_x_COEFF
NO
SEE PHASE
CALIBRATION
SECTION
To match all current channel, apply the same fixed input current to
all six channels. This should be the nominal current as described
in the Required Input Conditions section. The current rms
readings can then be used to determine if there is any error
between the six channels. For increased stability, synchronize
the rms register readings to the ZX measurement. This reduces
the effects of ripple in the readings caused by nonidealities of
the internal filtering. See the ADE7816 data sheet for details on
zero-crossing detection.
DOES
THE METER
ACCURACY MEET
SPECIFICATION
OVER POWER
FACTOR?
YES
SET
Wh/LSB
SEE ESTABLISHING
THE Wh/LSB
CONSTANT–FIRST
METER ONLY
SECTION
CALCULATION REQUIRED
ON FIRST METER ONLY.
THE SAME VALUE CAN
THEN BE USED ON ALL
SUBSEQUENT METERS
One channel, for example, Channel A, should be used as a
reference. The IBGAIN (Address 0x4382), ICGAIN (Address
0x4383), IDGAIN (Address 0x4384), IEGAIN (Address
0x4385) and IFGAIN (Address 0x4386) registers can then be
used to correct any mismatch from Channel A. The following
equation describes how to adjust the IxRMS reading to match
that in IARMS using the IxGAIN register:
CALIBRATE
xWGAIN
SEE ACTIVE
ENERGY GAIN
CALIBRATION
SECTION
IARMS 
−1
IxGAIN = 2 23 × 
 IxRMS 
CALIBRATE
xVARGAIN
After all IxGAIN register have been set, all six channels should
produce exactly the same IxRMS reading with a constant input.
SEE REACTIVE
ENERGY GAIN
CALIBRATION
SECTION
PHASE CALIBRATION
CALIBRATE
xWATTOS
SEE ACTIVE
ENERGY OFFSET
CALIBRATION
SECTION
NO
Phase calibration is required when the current sensor being
used introduces a phase shift. Current transformers can add
significant phase shift that introduces large errors at low power
factors. Phase calibration should be performed before gain or
offset calibration because large phase corrections can alter the
gain response of the ADE7816.
DOES THE
METER
ACCURACY MEET
SPECIFICATION
AT LOW
CURRENT?
YES
Phase calibration can be performed with a single inductive or
capacitive load at a power factor of 0.5. If this load is not available,
another power factor can be chosen; however, for best results,
the power factor should be as close to 0.5 as possible. The following
equation outlines how to determine the phase error in degrees:
CALIBRATE
xVAROS
ENERGY
CALIBRATION
COMPLETE
Figure 2. Active Energy Calibration Flow
10668-002
SEE REACTIVE
ENERGY OFFSET
CALIBRATION
SECTION
 AWATTHR sin(ϕ ) − AVARHR cos(ϕ ) 

Error(degrees) = tan −1 
 AVARHR sin(ϕ ) + AWATTHR cos(ϕ ) 
where φ refers to the angle between the voltage and the current
(in degrees).
Rev. 0 | Page 5 of 12
AN-1152
Application Note
For example, if a LINECYC value of 500 half line cycles is set
and the frequency of the input signal is 50 Hz, the accumulation
time is 5 seconds (0.5 × (1/50) × 500). Assuming that a load of
220 V and 10 A at a power factor of 0.5 (inductive) produces an
AWATTHR reading of 1870, and the AVARHR reading is
−3328, the error in degrees can be determined as follows:
 1870 sin(−60) + 3328 cos(−60) 
Error(degrees) = tan −1 

 − 3328 sin(−60) + 1870 cos(−60) 
= 0.668o
The ADE7816 uses all pass filters to accurately add time advances
and delays to the current channels with respect to the voltage
channels. A separate filter is included on each of the six current
channels. To adjust the time delay or advance, the coefficient of
these filters must be adjusted. Equation 1, Equation 2, and
Equation 3 show how the coefficients correspond to the phase
offset in radians.
PCF_x_COEFFFRACTION =
sin(error(θ ) + 3ω ) − sin ω
sin(error(θ ) + 4ω )
(1)
where error(θ) is the phase error in degrees.
ω = 2π
To determine the Wh/LSB constant, use the following formula:
Wh / LSB =
For example, if a LINECYC value of 500 half line cycles is set
and the frequency of the input signal is 50 Hz, the accumulation
time is 5 seconds (0.5 × (1/50) × 500). Assuming a load of 220 V
and 10 A produces an AWATTHR reading of 1909, the Wh/LSB
constant can be calculated as
Wh / LSB =
220 V ×10 A × cos(60) × 5 sec
1909 × 3600
= 8 ×10 −4
To adjust the constant to meet a particular specification or to
make the constant easier to store, the AWGAIN register can be
used. The AWGAIN register can be used to modify the Wh/LSB
constant by ±50%. The AWGAIN register affects the AWATTHR
register as shown in the following formula:
 AWATTHREXPECTED 
− 1
AWGAIN = 2 23 × 
 AWATTHRACTUAL

8000
If PCF_x_COEFF ≥ 0, then
PCF_x_COEFF = 223 × PCF_x_COEFFFRACTION
(2)
To achieve a different meter constant, alter the AWATTHR
reading based on the desired Wh/LSB.
If PCF_x_COEFF < 0, then
AWATTHREXPECTED =
PCF_x_COEFF = (2 + 23 ) × PCF_x_COEFFFRACTION
(3)
28
Using the previous example, the required phase adjustment, θ,
is 0.668°. The PCF_A_COEFF register setting can then be
calculated as follows:
ω = 2π
AWATTHR × 3600 sec/hr
where:
Accumulation Time is the line-cycle accumulation time.
AWATTHR is the energy register reading after this time has
elapsed.
Linefreq (Hz)
23
Load (W ) × Accumulation Time (sec)
50
= 0.039
8000
Load (W ) × Accumulation Time (sec)
Wh / LSB × 3600 sec/hr
For example, to alter the previously calculated Wh/LSB constant
to 9 × 10−4, the desired AWATTHR reading is:
AWATTHREXPECTED =
220 V ×10 A × cos(60) × 5 sec
PCF_A_COEFFFRACTION =
sin(0.668 + 3ω ) − sin ω
= 0 x 53502
sin(0.668 + 4ω )
9 ×10 −4 × 3600 sec/hr
= 1698 decimal
This adjustment can be made using the AWGAIN register as
described in the Active Energy Gain Calibration section.
PCF_A_COEFF = 2 × 0x53502 = 0x447B89
23
Analog Devices provides a spreadsheet to simplify this
calculation. It is available at
http://www.analog.com/ADE7816_tools_software_simulation.
Depending on the current sensors being used, different phase
calibration values can be required on all six channels.
ESTABLISHING THE WH/LSB CONSTANT—FIRST
METER ONLY
When calibrating the first meter, the Wh/LSB constant must be
determined. The Wh/LSB constant is used to set the weighting
of each LSB in the active energy register. This constant allows
the energy register readings to be converted into real-world values.
Once established, the same Wh/LSB meter can be used for each
subsequent meter.
ACTIVE ENERGY GAIN CALIBRATION
The purpose of the active energy gain calibration is to compensate
for small gain errors due to part-to-part variation in the internal
reference voltage and external components such as the time error
introduced by the crystal. Gain calibration is required on every
meter and is performed with nominal voltage and current inputs at
a power factor of 0.5 as previously described. For simplicity, it
is recommended that all meters be calibrated to use the same
Wh/LSB value, and this should be set up in the first meter as
explained in the Establishing the Wh/LSB Constant—First
Meter Only section.
Rev. 0 | Page 6 of 12
Application Note
AN-1152
Use the following formula to determine the expected reading in
the AWATTHR register:
AWATTHREXPECTED =
Load (W ) × Accumulation Time (sec)
Wh / LSB × 3600 sec/hr
The actual value can then be read from the AWATTHR register,
and the AWGAIN register can be used to correct any error. The
following formula shows how AWGAIN can be used to adjust
the AWATTHR reading:
 AWATTHREXPECTED 
− 1
AWGAIN = 2 23 × 
 AWATTHRACTUAL

Using the previous example, at 220 V and 10 A, the expected
AWATTHR reading is 1698 decimal. Assuming that the actual
AWATTHR reading is 1600 decimal, AWGAIN is calculated as
1698 
AWGAIN = 2 23 × 
− 1 = 0x7D70A
 1600 
Note that the gain calibration for Channel B through Channel F
is controlled by the BWGAIN, CWGAIN, EWGAIN, and
FWGAIN registers. Assuming that the channels are correctly
matched, as described in the Current Channel Gain Matching
section, the previous procedure does not need to be repeated for
the other channels. Write the value calculated for AWGAIN to
BWGAIN, CWGAIN, EWGAIN, and FWGAIN for accurate
results.
REACTIVE ENERGY GAIN CALIBRATION
Because the ADE7816 active and reactive energy measurements
are closely matched, separate reactive energy gain calibration is not
always required. In most cases, the values calculated for AWGAIN
in the Active Energy Gain Calibration section can be written to
the AVARGAIN register to retain the same VARhr/LSB constant.
If a different LSB weighting (that is, VARhr/LSB constant) or
further calibration is required, the reactive energy can be
calibrated separately. Reactive energy calibration should be
performed with nominal inputs at a power factor of 0.5 as
previously described. The reactive energy calibration is performed in a similar manner to the active energy calibration by
first determining the expected xVARHR output.
correctly matched, as described in the Current Channel Gain
Matching section, the previous procedure does not need to be
repeated for the other channels. Write the value calculated for
AVARGAIN to BVARGAIN, CVARGAIN, EVARGAIN, and
FVARGAIN for accurate results.
ADVANCED ENERGY OFFSET CALIBRATION
(OPTIONAL)
Active Energy Offset Calibration
Active energy offset calibration is required only if accuracy at low
loads is outside the required specification prior to offset
calibration.
To correct for any voltage-to-current channel crosstalk that may
degrade the accuracy of the measurements at low current levels,
perform active energy offset calibration. A low level current
signal must be applied to allow the offset magnitude to be
measured and then removed.
When performing offset calibration, it is often required to increase
the accumulation time to minimize the resolution error. As the
line-cycle accumulation mode accumulates energy over a fixed
time, the result is accurate to ±1 LSB. If the number of bits
accumulated in the xWATTHR register is small after this time,
the ±1 LSB error can result in a large error in the output. For
example, if only 10 bits are accumulated in the xWATTHR
register, the resolution error is 10%. Increasing the number of
accumulation bits to 1000 reduces the resolution error to 0.1%.
In the following example, a LINECYC value of 5000 half line
cycles is set, and an input current of 100 mA is applied. With a
voltage channel input of 220 V at a power factor of 0.5, the
expected AWATTHR reading is determined as
AWATTHREXPECTED =
220 V × 0.1 A × cos(60) × 50 sec
3 ×10 −5 × 3600
= 169
If the actual AWATTHR register reading is 165 at 100 mA, the
percentage error due to offset is determined as
% Error =
165 − 169
= −2.8%
169
The offset in the watt measurement is corrected according to
AWATTOS =
xVARHREXPECTED =
− %error ×
Load (VAR) × Accumulation Time (sec)
VARhr / LSB × 3600 sec/hr
AWATTHREXPECTED
WHTHR
×
8 kHz
AccumulationTime (sec)
AWATTOS = 0.028 ×
The compensation can then be determined by
 RENERGYAEXPECTED 
− 1
AVARGAIN = 223 × 
 RENERGYAACTUAL

Note that the gain calibration for Channel B through Channel F
is controlled by the BVARGAIN, CVARGAIN, EVARGAIN,
and FVARGAIN registers. Assuming that the channels are
169 0x2000000
×
= 0x18E
50
8 kHz
Note that, depending on the board layout and the crosstalk on
the meter design, Channel B through Channel F may need a
separate offset calibration from Channel A. This can be achieved
through the BWATTOS, CWATTOS, DWATTOS, EWATTOS,
and FWATTOS registers. These registers correct the respective
Rev. 0 | Page 7 of 12
AN-1152
Application Note
xWATTHR register reading in the same way that AWATTOS
affects the AWATTHR register reading.
may also be required on every meter to remove crosstalk that
may degrade the accuracy of the readings at low signal inputs.
Reactive Energy Offset Calibration
RMS Gain
Reactive energy offset calibration is only required if accuracy at low
loads is outside the required specification prior to offset calibration.
Along with compensating for part-to-part gain variations, the
rms gain constant converts the rms reading in LSBs into a
current or voltage value in amps or volts. The voltage and current
rms constants are determined under fixed load conditions by
dividing the number of LSBs in the rms register by the amplitude of the input.
To correct for any voltage-to-current channel crosstalk that may
degrade the accuracy of the measurements at low current levels,
reactive energy offset calibration is performed. A low level current
signal must be applied to allow the offset magnitude to be
measured and then removed.
When performing offset calibration, it is often required to increase
the accumulation time to minimize the resolution error. Because
the line-cycle accumulation mode accumulates energy over a
fixed time, the result is accurate to ±1 LSB. If the number of bits
accumulated in the xVARHR register is small after this time, the
±1 LSB error can result in a large error in the output. For example,
if only 10 bits are accumulated in the xVARHR register, the resolution error is 10%. Increasing the number of accumulation bits
to 1000 reduces the resolution error to 0.1%. The expected
xVARHR reading is determined as
AVARHREXPECTED =
Load (VAR) × Accumulation Time (sec)
VARhr / LSB × 3600 sec/hr
The offset in the reactive energy measurement is corrected
according to the following equation:
AVAROS =
RENERGYAEXPECTED
WTHR
− % Error ×
×
Accumulatiom Time (sec) 8 kHz
Note that, depending on the board layout and the crosstalk on
the meter design, Channel B through Channel F may need a
separate offset calibration from Channel A. This can be achieved
through the BVAROS, CVAROS, DVAROS, EVAROS, and
FVAROS registers. These registers correct the respective xVARHR
register reading in the same way that AVAROS affects the
AVARHR register reading.
CURRENT AND VOLTAGE RMS
Calibrating the voltage and current rms is only required if the
instantaneous rms readings are required. RMS calibration does
not affect the performance of the active or reactive energy.
Perform the rms calibration using the instantaneous rms register readings. The readings can be obtained from the IxRMS
register and the VRMS register. For increased stability, synchronize the rms register readings to the ZX measurement. This
reduces the effects of ripple in the readings caused by the
nonidealities of the internal filtering. See the ADE7816 data
sheet for details on zero-crossing detection.
V Constant [V/LSB] =
Voltage Input [V]
VRMS[LSBs]
I Constant [Amps/LSB] =
×k
Current Input [A]
IxRMS[LSBs]
×k
If the current channels have been correctly matched by following the procedure described in the Current Channel Gain
Matching section, all current channels, A through F, should
have the same I constant.
To maintain the full resolution when the conversion is taking place
in the firmware, the voltage and current rms constants can be
multiplied by a constant, k. The use of a multiplication factor, k,
allows resolution to be maintained when converting and storing
the rms readings as a hexadecimal number using fixed point
multiplication. Converting the reading to the hexadecimal format
is required prior to performing a hexadecimal-to-binary coded
decimal conversion for display purposes.
An example of how the voltage rms register reading can be
converted into a value in volts, while maintaining resolution of
one digit below the decimal point, is provided in the following
equation. In this example, 220 V is applied, producing a VRMS
register reading of 3,400,000 decimal.
V Constant =
220 V
×100 × 216 = 0 x1A8
3,400,000
The volts/LSB constant is multiplied by a factor of 100 × 216 to
maintain accuracy when using fixed point multiplication. The
V constant is 0x1A8.
An additional example showing the generation of the current rms
gain constant is provided in the following equation. In this
example, the resulting LCD display measurement is accurate to
two digits below the decimal point. A current input of 10 A is
applied, resulting in an IRMS reading of 400,000 decimal.
I Constant =
10 A
×1000 × 216 = 0 x 666
400,000
The amps/LSB constant is multiplied by a factor of 1000 × 216 to
maintain the required accuracy during conversion. The resulting
I constant is 0x666.
The current and voltage rms readings require gain calibration to
compensate for any part-to-part variations. Offset calibration
Rev. 0 | Page 8 of 12
Application Note
AN-1152
RMS Offset
To obtain accurate readings at low signal levels, the current and
voltage rms offset may have to be calibrated. This calibration is
performed using the internal VRMSOS and IxRMSOS registers
that apply an offset prior to the square root function. The
compensation factor is determined by applying the following
equations:
VRMSEXPECTED 2 − VRMSACTUAL 2
212
IxRMSOS =
IRMSEXPECTED 2 − IRMSACTUAL 2
212
NOMINAL READING
INPUT AMPLITUDE
ACTUAL RMS
OFFSET
ERROR
10668-003
VRMSOS =
As illustrated in Figure 3, the rms offset calibration is based on
two points, where the expected reading is derived from the rms
measurement with nominal inputs.
EXPECTED RMS
Figure 3. RMS Offset Compensation
Rev. 0 | Page 9 of 12
AN-1152
Application Note
NOTES
Rev. 0 | Page 10 of 12
Application Note
AN-1152
NOTES
Rev. 0 | Page 11 of 12
AN-1152
Application Note
NOTES
I2C refers to a communications protocol originally developed by Philips Semiconductors (now NXP Semiconductors).
©2012 Analog Devices, Inc. All rights reserved. Trademarks and
registered trademarks are the property of their respective owners.
AN10668-0-5/12(0)
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